## Largest prime factors of consecutive numbers

### Problem 526

Let `f`(`n`) be the largest prime factor of `n`.

Let `g`(`n`) = `f`(`n`) + `f`(`n`+1) + `f`(`n`+2) + `f`(`n`+3) + `f`(`n`+4) + `f`(`n`+5) + `f`(`n`+6) + `f`(`n`+7) + `f`(`n`+8), the sum of the largest prime factor of each of nine consecutive numbers starting with `n`.

Let `h`(`n`) be the maximum value of `g`(`k`) for 2 ≤ `k` ≤ `n`.

You are given:

`f`(100) = 5`f`(101) = 101`g`(100) = 409`h`(100) = 417`h`(10^{9}) = 4896292593

Find `h`(10^{16}).